366 research outputs found
Development of Probabilistic Cardinal Models
Cardinal models solve problems of the form Y=X_1+X_2+...+X_n, where we have discrete distributions on each random variable. The objective was to improve the usability and performance of Evergreen, an engine for solving cardinal models and to create cardinal models using them
Adversarial network training using higher-order moments in a modified Wasserstein distance
Generative-adversarial networks (GANs) have been used to produce data closely
resembling example data in a compressed, latent space that is close to
sufficient for reconstruction in the original vector space. The Wasserstein
metric has been used as an alternative to binary cross-entropy, producing more
numerically stable GANs with greater mode covering behavior. Here, a
generalization of the Wasserstein distance, using higher-order moments than the
mean, is derived. Training a GAN with this higher-order Wasserstein metric is
demonstrated to exhibit superior performance, even when adjusted for slightly
higher computational cost. This is illustrated generating synthetic antibody
sequences
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Conic Sampling: An Efficient Method for Solving Linear and Quadratic Programming by Randomly Linking Constraints within the Interior
Linear programming (LP) problems are commonly used in analysis and resource allocation, frequently surfacing as approximations to more difficult problems. Existing approaches to LP have been dominated by a small group of methods, and randomized algorithms have not enjoyed popularity in practice. This paper introduces a novel randomized method of solving LP problems by moving along the facets and within the interior of the polytope along rays randomly sampled from the polyhedral cones defined by the bounding constraints. This conic sampling method is then applied to randomly sampled LPs, and its runtime performance is shown to compare favorably to the simplex and primal affine-scaling algorithms, especially on polytopes with certain characteristics. The conic sampling method is then adapted and applied to solve a certain quadratic program, which compute a projection onto a polytope; the proposed method is shown to outperform the proprietary software Mathematica on large, sparse QP problems constructed from mass spectometry-based proteomics
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